Chip design with iterative fabrication cycles is expensive and quite slow. Fabrication steps involve processes such as lithography, doping, etching, chemical mechanical polishing, and the like. Manufacturing processes, however, are not deterministic, and have inherent random and systematic variability built into them. Design-for-Manufacturing (DfM) methods can predict and/or project fabrication results using fully-software-based tools. Technology Computer-Aided Design (TCAD) tools can be one of the key components of DfM. However, numerical device simulations (i.e., TCAD) are based on solving drift-diffusion or hydrodynamic transport equations which are forms of partial differential equations. One example of such simulations is the MEDICI: 2-D Device Simulation tool available from Synopsys Inc., Mountain View, Calif., USA.
Furthermore, device and/or circuit mix-mode simulations consume additional effort and more time, so TCAD tools cannot be directly used in circuit analysis. TCAD-embedded statistical analysis cannot be applied in the DfM world due to computational time and a weak TfM (TCAD for manufacturability) infrastructure. TCAD simulations and methods have expensive computational times and cannot be directly inserted into DfM flows.
Prior art techniques have focused on “SPICE compact models” for the device or the device variability to study design yield.